Download Problem Due Wednesday 5 PM EST Exercise 1.1: Classifying

Problem
Due Wednesday 5 PM EST
Exercise 1.1: Classifying Variables
For each of the following variables:
Tell whether the variable is quantitative or categorical, identify the observational units, if
the variable is quantitative, and tell whether it is continuous or discrete.
a)
b)
c)
d)
e)
f)
The month a person is born
The amount of money a person has on his/her person
The color of an M&M candy taken from a bag
The number of grams of fat in a cookie
The amount of time a car waits at the drive-through of a fast food restaurant
The number of M&M candies in a 10 oz. bag
Exercise 1.5: Placement Exam Scores
Adapted from Allan J. Rossman, Beth L. Chance, and Robin H. Lock, Workshop Statistics: Discovery with Data and
Fathom (Key College Publishing, 2001), 59
The Department of Mathematics and Computer Science at Dickinson College gives an
exam each fall to freshman who intend to take calculus. The scores on the exam are used
to determine into which level of calculus a student should be placed. The exam consists
of 20 multiple-choice questions. Scores for the 213 students who took the exam in 1992
are found in the Excel File, MathPlacementScores.xls.
a) What is/are the variable(s)? Classify as categorical or quantitative.
b) This is the dot plot of this distribution. List at least two conclusions you make
from this display.
c) Create a histogram you feel best summarizes the distribution. Justify your choice.
This applet may be useful:
http://www.zweigmedia.com/RealWorld/stats/histogram.html
You may also make a Histogram in Excel, or by hand.
Take a screen shot or picture of your histogram and include it in your answers.
d) Give an interval of “typical” scores for this group. Briefly describe why you chose
this interval (why you believe it is typical). Include your estimate of the
probability that a student would score in this interval, and explain why you feel it
is a good estimate.
Exercise 1.6: DoW #3 Collection Tool
Compare the number of raisins in a box for two different brands of raisins.
a) Summarize the method your group used to collect the data. Provide rationale for
decisions your group made.
b) Evaluate the effectiveness of your tool. Do you think your tool collected quality
data? Why or why not? (Be sure to discuss possible sources of bias in your
response to this question)
YOU WILL ANSWER 1.6 BASED ON THE DATA BELOW
Question:
Does the number of raisins in a ½ ounce box of raisins
differ for a store-brand box of raisins and a name-brand
box of raisins?
1. Store box versus name brand raisins ( categorical)
Variables:
2. the number of raisins ( quantitative)
3. size of box ( quantitative) – constant variable
1. Equal number of the boxes of raisins( store bought and
brand name.
- If we cannot get ½ ounce boxes of raisins then
Observational units:
We would have to measure quantity of raisins per
ounce in name brand and non-name brand.
2. The stores that the raisins were bought.
Type of study:
Expected difference:
Sampling Strategy:
This is clearly an observational study, as the researcher
would be required to choose randomly samples of both
store bought and brand name raisins and count the number
of raisins in each.
We suspect that there will be a difference, but not
significant. We think that the raisin boxes from both store
brand and brand name may not contain equal number of
raisins. For example two boxes of Sun –maid raisins may
not contain the same number of raisins.
We think stratified random sampling would be a better
approach to ensure that we have a representative number
from both store box and brand name.
So we would first randomly choose 30 – ½ ounce boxes
of store brand raisins and 30 – ½ ounce boxes of brand
name raisins.
Potential bias:
Since not all the group members have access to the same
store brand raisins then there may be a bias.
1. Research to find out the brand of raisins that are
available.
2. We could each pick a brand and be responsible for that,
or we could have two people do store brand (different or
the same), and two people do the name brand
Our plan:
3 buy multiples boxes from the same brand at the same
store.
4. We will count and record the number of raisins in each
box.
5. We will share our data in a table or spreadsheet format.
6 We will analyses our findings